a. Let  where a is a real number. Evaluate I(a) and show that its value is independent of a. Split the integral into two integrals over [0, 1] and [1, ∞]; then use a change of variables to convert the second integral into an integral over [0, 1].)

b. Let f be any positive continuous function on [0, π/2]. Evaluate 

Use the identity cos (π/2 - x) = sin x.)

Transcribed Image Text:

dx I(a) (1 + xª)(1 + x²)’ 18 || 7/2 f(cos x) -dx. Jo f(cos x) + f(sin x)